When the Giants drafted Lorenzo Carter in the spring, he was well-versed in the team’s legacy of pass-rushers. It’s a chain that goes back to Lawrence Taylor, who played with Michael Strahan, who played with Osi Umenyiora and Justin Tuck, who played with Jason Pierre-Paul.

Just about every time the Giants have drafted a defensive end (or an outside linebacker like Carter, now that they are a 3-4 scheme) in the past few years, he’s said exactly what Carter said about knowing the team’s history at the position and wanting to be the next link in that chain. For various reasons, they were unable to continue the tradition. Damontre Moore, a third-round pick in 2013, lasted two-and-a-half seasons and had 8 1/2 sacks but was released after a locker room fight. Owa Odighizuwa, a fourth-rounder, played two seasons with the Giants and never registered a sack before deciding to walk away from the team last offseason.

It’s left that chain of homegrown pass-rushers broken for the first time since 1982. When the Giants traded Pierre-Paul this offseason, he was the last direct link in that three-and-a-half decade run. The Giants have Olivier Vernon and Connor Barwin and Kareem Martin out there now, but they’ve all come as free agents. The franchise that always said it could never draft enough pass-rushers finds itself without a proven one on its current roster.

Unless, of course, Carter can pick up the slack. He has a chance to do what Moore and Odighizuwa wanted to do but could not, to follow in the footsteps of Giants draft picks who developed into ferocious and sometimes dominant pass-rushers.

“That,” Carter said, “is definitely the goal.”

He’s shown flashes of it in training camp, enough to excite the Giants' coaches.

“Lorenzo’s really had a couple of good practices and as in any rookie, the challenge is to stack them,” defensive coordinator James Bettcher said. “It’s not to have one day and flash, it’s to have two days. Do we see those corrections happen and do we see it continue to get better?”

Carter, a sleek edge rusher, did not put up massive statistical numbers at Georgia. He had just 14 sacks in four seasons there. But he was also asked to do many more things as a player in college. With the Giants, at this point, he’s essentially being asked to do one thing on defense: Get after the passer.

“You just get to play ball, just go in there and wreck stuff,” Carter said when asked why he likes the Giants’ defensive scheme. “It doesn’t matter how pretty it is, just get the job done, try to knock people off the ball, and go play.”

Of course, there are improvements that need to be made. Carter isn’t expecting to be a great pass rusher from the start.

“Just come in humble and working, willing to work, and take coaching,” he said of his mindset. “I just try to do what coaches tell me. They put me in the best position and the athleticism and all the other stuff that is God-given and worked for, that takes care of itself on the field when you are out there just playing fast. The coaches will put you in the best position so I’m just trying to listen to them and do what they say.”

If he can, he may be able to pick up the mantle that has fallen and become the Giants’ next great homegrown pass-rusher.

“If I came in drafted, undrafted, it doesn’t matter,” he said. “I want to be that guy who can help make plays and can help lead this defense and this team to a championship.”

They all say that. Whether or not Carter can do it will determine his legacy and his place in the team’s.